Question

A box contains four slips of paper marked 9, 10, 11, and 12. Two slips are selected without replacement. List the possible values for each of the following random variables shown below:

(a) x = sum of the two numbers

20, 21, 23, 24, 26

20, 22, 24, 26, 28

   9, 10, 11, 12, 13

19, 20, 21, 22, 23

19, 21, 23, 25, 27

(b) y = difference between the first and second numbers

-3, -1, 1, 3

-5, -3, -1, 1, 3, 5

-3, -2, -1, 1, 2, 3

-4, -3, -2, 2, 3, 4

-2, -1, 1, 2

(c) z = number of slips selected that show an even number

0, 2

2, 4   

0, 1, 2

1, 2

0, 1

(d) w = number of slips selected that show a 9

0

2    

1

0, 1

1, 2

Answer 1

(a) 19, 20, 21, 22, 23

(b) -3, -2, -1, 1, 2, 3

(c) 0, 1, 2

(d) 0, 1

Justufications

(a)

X=sum of two numbers.

X can take the possible values 9+10,9+11,9+12,10+11,10+12,11+12

ie X can take values 19,20,21,22,23

(b)

Y=Difference between first and second numbers.

Y can take the possible values 9-10,9-11,9-12,10-9,10-11,10-12,11-9,11-10,11-12,12-9,12-10,12-11

ie Y can take values -1,-2,-3,1,2,3

(c) z = number of slips selected that show an even number

If the numbers shown are 9 and 11, Z=0

If numbers shown iare 9,10 or 9,12 or 11,10 or 11,12 then Z=1

If numbers shown are 10 and 12 Z=2

So the possible values of Z are 0,1,2

(d) w = number of slips selected that show a 9

Since we are selecting slips without replacement 9 can occur at most 1 time.

If the numbers are 10,11 or 10,12 or 11,12, there will be no 9 and w=0

So the possible values of w are 0,1